Mathematical Geometry

数学几何

• 批准号: 60302003
• 负责人: OMORI Hideki
• 金额: $ 6.21万
• 依托单位: Science University of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Co-operative Research (A)
• 财政年份: 1985
• 资助国家: 日本
• 起止时间: 1985 至 1986
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-60302003/
• 关键词: MANIFOLD; NONLINEAR PARTIAL DIFFERENTIAL EQUATION; 非可換微分幾何

A finite dimensional manifold was a traditional, basic concept with which one could begin differential geometry. However, we are feeling that differential geometry is now facing a great philosophical turnint point. We have to construct differential geometry on some other basic concept than finite dimensional manifolds.Another word, one has to try to construct a sort of "Pointless Geometry" of Von Neumann, or a sort of "Noncommutative Geometry" of Conne. Needless to say, these exist only in the brain of few genius.To reveal it, and to make Japanese geometers recoginize it, we had to organize a lot of meetings at various places in Japan, which involve several physicists especially field-theoretists. We did it in this project. There were 19 meetings held in the last two years.In these meetings, Japanese geometers recoginized that differential geometry and field theory especially string model theory in physics have a common problem and a common philosophy.

有限维流形是一个传统的基本概念，人们可以用它开始微分几何。然而，我们感到微分几何现在面临着一个重大的哲学转折点。我们必须在有限维流形之外的其他一些基本概念上构造微分几何。换句话说，我们必须尝试构造一种冯·诺依曼的“无意义几何”，或者一种康奈的“非交换几何”。不用说，这些只存在于少数天才的大脑中。为了揭示它，为了让日本几何学家认识它，我们不得不在日本各地组织很多会议，其中包括几位物理学家特别是场理论家。我们在这个项目中做到了。近两年共召开了19次会议。在这些会议中，日本几何学家们认识到微分几何和场论特别是物理学中的弦模型理论有一个共同的问题和共同的哲学。

项目成果

TOSHIAKI ADACHI;TOSHIKAZU SUNADA: Journal of Differential geometry. 22. (1987)

Toshiaki ADACHI；TOSHIKAZU SUNADA：微分几何杂志。

TOSHIAKI ADACHI, TOSHIKAZU SUNADA: "Homology of closed geodesics in a negatively curved manifold" Journal of differential geometry. 22. (1987)

Toshiaki ADACHI、TOSHIKAZU SUNADA：“负曲流形中闭合测地线的同调”微分几何杂志。

HIROO MASUDA: "On n-dimensional LOrentz manifolds admitting an isometry group of dimension n(n-1)/2 for n <=!>> 4." Hokkaido Mathematical Journal. 15. 309-315 (1986)

HIROO MASUDA：“在 n 维洛伦兹流形上，对于 n <=!>> 4，承认维度为 n(n-1)/2 的等距群。”

OSAMU KOBAYASHI;AKIRA YOSHIOKA;YOSHIAKI MAEDA;HIDEKI OMORI: Acta Applicandae Mathematicae. 3. 71-106 (1985)

小林修；吉冈彰；前田吉明；大森英树：数学应用学报。

W.KLINGENBERG, TAKASHI SAKAI: "Remarks on the injectivity radius estimate for almost 1/4-pinched manifolds" Lecture Note in Mathematics, Springer. 1201. 156-164 (1986)

W.KLINGENBERG、TAKASHI SAKAI：“关于几乎 1/4 收缩流形的注入半径估计的评论”数学讲义，Springer。